Times to Service Completion and Abandonment in the M/M/m Preemptive LCFS Queue with Impatient Customers

We consider the M/M/m preemptive last-come, first-served queue without customer's priority classes. We focus on the analysis of the time interval from the arrival to either service completion or to abandonment of an arbitrary customer. We formulate the problem as a one-dimensional birth-and-death process with two absorbing states and consider the first passage times in this process. We give explicit expressions for the probabilities of service completion and abandonment. We also show sets of recursive computational formulas for calculating the mean and second moment of the times to service completion and abandonment. We present some numerical examples in order to demonstrate the computation of theoretical formulas.